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56
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56 is an integer, the number of reduced 5 by 5 Latin squares (see A000315).
Contents
Membership in core sequences
Even numbers | ..., 50, 52, 54, 56, 58, 60, 62 ... | A005843 |
Composite numbers | ..., 52, 54, 55, 56, 57, 58, 60, ... | A002808 |
Abundant numbers | ..., 42, 48, 54, 56, 60, 66, 70, ... | A005101 |
Partition numbers | ..., 22, 30, 42, 56, 77, 101, ... | A000041 |
Tetrahedral numbers | 1, 4, 10, 20, 35, 56, 84, 120, ... | A000292 |
Oblong numbers | ..., 20, 30, 42, 56, 72, 90, 110, ... | A002378 |
Quarter-squares | ..., 36, 42, 49, 56, 64, 72, 81, ... | A002620 |
Central polygonal numbers | ..., 29, 37, 46, 56, 67, 79, 92, ... | A000124 |
In Pascal's triangle, 56 occurs four times, the first two times on row 8 as the sum of 21 and 35 from row 7.
Notice 56 as a denominator in this continued fraction (A002530):
Also .
Sequences pertaining to 56
Divisors of 56 | 1, 2, 4, 7, 8, 14, 28, 56 | A018265 |
Multiples of 56 | 0, 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, ... | |
sequence starting at 36 | 36, 18, 9, 26, 13, 38, 19, 56, 28, 14, 7, 20, 10, 5, 14, 7, 20, ... | A008894 |
sequence starting at 99 | 99, 298, 149, 448, 224, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, ... | A008882 |
sequence starting at 5 | 5, 26, 13, 66, 33, 11, 56, 28, 14, 7, 36, 18, 9, 3, 1, 6, 3, 1, ... | A057688 |
Partitions of 56
There are 526823 partitions of 56.
The Goldbach representations of 56 are: 3 + 53 = 13 + 43 = 19 + 37.
Roots and powers of 56
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Values for number theoretic functions with 56 as an argument
0 | ||
−2 | ||
16 | ||
120 | ||
8 | ||
24 | ||
4 | ||
2 | ||
6 | This is the Carmichael lambda function. | |
1 | This is the Liouville lambda function. |
Factorization of 56 in some quadratic integer rings
As was mentioned above, 56 is composite in . But it has different factorizations in some quadratic integer rings.
TABLE GOES HERE
Representation of 56 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 111000 | 2002 | 320 | 211 | 132 | 110 | 70 | 62 | 56 | 51 | 48 | 44 | 40 | 3B | 38 | 35 | 32 | 2I | 2G |
See also
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |
1729 |